It is conventional to use the full forms of words and phrases. Contractions and abbreviations create a more informal and colloquial tone, and are more common in spoken language, informal written communication, and note-taking.
- Contractions. Contracted forms such as isn't, he's, it'll are informal usage. The apostrophe is used to indicate the missing letters.
There is often confusion about the use of the apostrophe in the similar words its and it's. However, the version with the apostrophe (it's) is a contraction of it is, and should therefore be avoided in academic writing. The possessive its (e.g. "the metaphor derives its impact") is acceptable, and commonly used.
- Abbreviations. Shortened forms of expressions such as e.g., etc., N.B. are not used frequently.
If you do use them, make sure your punctuation is correct. You could write them in full, but expressions tend to be latinate in origin, and might sound slightly archaic: exempli gratia, et cetera, nota bene. Other, anglicised phrases are usually subtituted: such as, for example, and so on, it should be noted, etc. or similar phrases should be used with caution, to ensure that your writing is as precise as possible, and if you do ask your reader to note a point, remember to explain why it is significant. Symbols such as &, and numerals except for dates or page or line numbers (1, 2, 3) are not usually used in academic writing in English, but are short-cuts in note-taking.